Banach空间中GC(0,e)类广义发展算子的一致指数不稳定性

On uniform exponential instability of GC(0,e)-generalized evolution operator in Banach space

研究Bananch空间中GC(0,e)类广义发展算子的一致指数不稳定性。基于GC(0,e)类广义发展算子的定义,应用数学分析与算子理论得到了一致指数不稳定的若干充要条件刻画。所得结果推广和完善了指数稳定性理论中一些已有结果,这对于研究广义发展算子的不稳定性具有重要的理论价值。

The uniform exponential instability of GC(0,e)-generalized evolution operator in Banach space is studied.Based on the definition of GC(0,e)-generalized evolution operator,the necessary and sufficient conditions for uniform exponential instability are obtained via mathematical analysis and operator theory.The results extend some well-known results in exponential stability theory.The research is theoretically important for studying the instability of generalized evolution operator.